{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nonlinear Model Predictive Control with C-GMRES"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "image/png": {
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "Image(filename=\"Figure_4.png\",width=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "image/png": {
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename=\"Figure_1.png\",width=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 8,
     "metadata": {
      "image/png": {
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename=\"Figure_2.png\",width=600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "image/png": {
       "width": 600
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Image(filename=\"Figure_3.png\",width=600)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![gif](https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/cgmres_nmpc/animation.gif)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mathematical Formulation\n",
    "\n",
    "Motion model is\n",
    "\n",
    "$$\\dot{x}=vcos\\theta$$\n",
    "\n",
    "$$\\dot{y}=vsin\\theta$$\n",
    "\n",
    "$$\\dot{\\theta}=\\frac{v}{WB}sin(u_{\\delta})$$ (tan is not good for optimization)\n",
    "\n",
    "$$\\dot{v}=u_a$$\n",
    "\n",
    "Cost function is \n",
    "\n",
    "$$J=\\frac{1}{2}(u_a^2+u_{\\delta}^2)-\\phi_a d_a-\\phi_\\delta d_\\delta$$\n",
    "\n",
    "Input constraints are\n",
    "\n",
    "$$|u_a| \\leq u_{a,max}$$\n",
    "\n",
    "$$|u_\\delta| \\leq u_{\\delta,max}$$\n",
    "\n",
    "So, Hamiltonian　is\n",
    "\n",
    "$$J=\\frac{1}{2}(u_a^2+u_{\\delta}^2)-\\phi_a d_a-\\phi_\\delta d_\\delta\\\\ +\\lambda_1vcos\\theta+\\lambda_2vsin\\theta+\\lambda_3\\frac{v}{WB}sin(u_{\\delta})+\\lambda_4u_a\\\\ \n",
    "+\\rho_1(u_a^2+d_a^2+u_{a,max}^2)+\\rho_2(u_\\delta^2+d_\\delta^2+u_{\\delta,max}^2)$$\n",
    "\n",
    "Partial differential equations of the Hamiltonian are:\n",
    "\n",
    "$\\begin{equation*}\n",
    "\\frac{\\partial H}{\\partial \\bf{x}}=\\\\ \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial H}{\\partial x}= 0&\\\\\n",
    "\\frac{\\partial H}{\\partial y}= 0&\\\\\n",
    "\\frac{\\partial H}{\\partial \\theta}= -\\lambda_1vsin\\theta+\\lambda_2vcos\\theta&\\\\\n",
    "\\frac{\\partial H}{\\partial v}=-\\lambda_1cos\\theta+\\lambda_2sin\\theta+\\lambda_3\\frac{1}{WB}sin(u_{\\delta})&\\\\\n",
    "\\end{bmatrix}\n",
    "\\\\\n",
    "\\end{equation*}$\n",
    "\n",
    "\n",
    "$\\begin{equation*}\n",
    "\\frac{\\partial H}{\\partial \\bf{u}}=\\\\ \n",
    "\\begin{bmatrix}\n",
    "\\frac{\\partial H}{\\partial u_a}= u_a+\\lambda_4+2\\rho_1u_a&\\\\\n",
    "\\frac{\\partial H}{\\partial u_\\delta}= u_\\delta+\\lambda_3\\frac{v}{WB}cos(u_{\\delta})+2\\rho_2u_\\delta&\\\\\n",
    "\\frac{\\partial H}{\\partial d_a}= -\\phi_a+2\\rho_1d_a&\\\\\n",
    "\\frac{\\partial H}{\\partial d_\\delta}=-\\phi_\\delta+2\\rho_2d_\\delta&\\\\\n",
    "\\end{bmatrix}\n",
    "\\\\\n",
    "\\end{equation*}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ref\n",
    "\n",
    "- [Shunichi09/nonlinear\\_control: Implementing the nonlinear model predictive control, sliding mode control](https://github.com/Shunichi09/nonlinear_control)\n",
    "\n",
    "- [非線形モデル予測制御におけるCGMRES法をpythonで実装する \\- Qiita](https://qiita.com/MENDY/items/4108190a579395053924)"
   ]
  }
 ],
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